Faculty Bibliography

We propose and study a simple and innovative non-parametric approach to estimate the age-of-onset distribution for a disease from a cross-sectional sample of the population that includes individuals with prevalent disease. First, we estimate the joint distribution of two event times, the age of disease onset and the survival time after disease onset. We accommodate that individuals had to be alive at the time of the study by conditioning on their survival until the age at sampling. We propose a computationally efficient expectation-maximization (EM) algorithm and derive the asymptotic properties of the resulting estimates. From these joint probabilities we then obtain non-parametric estimates of the age-at-onset distribution by marginalizing over the survival time after disease onset to death. The method accommodates categorical covariates and can be used to obtain unbiased estimates of the covariate distribution in the source population. We show in simulations that our method performs well in finite samples even under large amounts of truncation for prevalent cases. We apply the proposed method to data from female participants in the Washington Ashkenazi Study to estimate the age-at-onset distribution of breast cancer associated with carrying BRCA1 or BRCA2 mutations.

Typically, case-control studies to estimate odds-ratios associating risk factors with disease incidence only include newly diagnosed cases. Recently proposed methods allow incorporating information on prevalent cases, individuals who survived from disease diagnosis to sampling, into cross-sectionally sampled case-control studies under parametric assumptions for the survival time after diagnosis. Here we propose and study methods to additionally use prospectively observed survival times from prevalent and incident cases to adjust logistic models for the time between diagnosis and sampling, the backward time, for prevalent cases. This adjustment yields unbiased odds-ratio estimates from case-control studies that include prevalent cases. We propose a computationally simple two-step generalized method-of-moments estimation procedure. First, we estimate the survival distribution assuming a semiparametric Cox model using an expectation-maximization algorithm that yields fully efficient estimates and accommodates left truncation for prevalent cases and right censoring. Then, we use the estimated survival distribution in an extension of the logistic model to three groups (controls, incident, and prevalent cases), to adjust for the survival bias in prevalent cases. In simulations, under modest amounts of censoring, odds-ratios from the two-step procedure were equally efficient as those estimated from a joint logistic and survival data likelihood under parametric assumptions. This indicates that utilizing the cases' prospective survival data lessens model dependencies and improves precision of association estimates for case-control studies with prevalent cases. We illustrate the methods by estimating associations between single nucleotide polymorphisms and breast cancer risk using controls, and incident and prevalent cases sampled from the US Radiologic Technologists Study cohort.

Among several semiparametric models, the Cox proportional hazard model is widely used to assess the association between covariates and the time-to-event when the observed time-to-event is interval-censored. Often, covariates are measured with error. To handle this covariate uncertainty in the Cox proportional hazard model with the interval-censored data, flexible approaches have been proposed. To fill a gap and broaden the scope of statistical applications to analyze time-to-event data with different models, in this paper, a general approach is proposed for fitting the semiparametric linear transformation model to interval-censored data when a covariate is measured with error. The semiparametric linear transformation model is a broad class of models that includes the proportional hazard model and the proportional odds model as special cases. The proposed method relies on a set of estimating equations to estimate the regression parameters and the infinite-dimensional parameter. For handling interval censoring and covariate measurement error, a flexible imputation technique is used. Finite sample performance of the proposed method is judged via simulation studies. Finally, the suggested method is applied to analyze a real data set from an AIDS clinical trial.

Investigators from a large consortium of scientists recently performed a multi-year study in which they replicated 100 psychology experiments. Although statistically significant results were reported in 97% of the original studies, statistical significance was achieved in only 36% of the replicated studies. This article presents a reanalysis of these data based on a formal statistical model that accounts for publication bias by treating outcomes from unpublished studies as missing data, while simultaneously estimating the distribution of effect sizes for those studies that tested nonnull effects. The resulting model suggests that more than 90% of tests performed in eligible psychology experiments tested negligible effects, and that publication biases based on p-values caused the observed rates of nonreproducibility. The results of this reanalysis provide a compelling argument for both increasing the threshold required for declaring scientific discoveries and for adopting statistical summaries of evidence that account for the high proportion of tested hypotheses that are false. Supplementary materials for this article are available online.